I have a 2003 Hyundai Elantra GT with 90000 miles and recently experienced a persistent burning smell, noticeable in the passenger compartment but coming from the front of the car. It turned out to be a failing hose clamp on a power steering fluid line coming out of the power steering reservoir and going into the engine (the bad clamp was on the engine side of this hose). It was apparently spraying a fine mist of power steering fluid (presumably only while driving/turning) all over. Despite the persistent leak, only a slight amount of power steering fluid was lost; the reservoir is still just barely below the MAX line. This fluid would get on the front of the engine block, and drip down near the oil filter. I don't think it ever got close to the exhaust. Just the heat of the engine block seems to be enough to vaporize this fluid. It's awful! Anyway, the solution was a new 5 dollar hose clamp followed by an 80 dollar engine steam clean.
Before discovering this issue, my mechanics tried several other remedies, including replacing the valve cover gasket to stop a tiny oil leak; replacing torn CV boots which were spattering grease on the underside of the car; replacing a bad exhaust manifold gasket which some white powder revealed to be leaking; and replacing a water pump that was leaking some coolant. All those repairs were needed, and most of these repairs helped reduce the burning smell. But it was the power steering hose clamp and subsequent engine steam clean that solved the issue.
